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first u add all the terms in question
u get
( a(b+c)^2+b(c+a)^2+c(a+b)^2)/abc
(b^2(a+c)+c^2(a+b)+a^2(c+b)+6abc)/abc
- hence it is given that a+b+c=0
- then a+c=-b
- a+b=-c
- b+c=-a
then after substituting this values in above equation we get
(-(b^3+a^3+c^3)+6abc )/abc
and also it is given that (a^3+b^3+c^3)=3abc
using this we get
(-3abc+6abc)/abc=3abc/abc=3
hence proved
shivi001:
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